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Stability of sessile and pendant liquid drops

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Abstract

The solution space of axisymmetric liquid drops attached to a horizontal plane is investigated, and the stability of hydrostatic shapes is assessed by a novel numerical linear stability analysis involving discrete perturbations. For a given contact angle and Bond number, multiple interfacial shapes exist with compact, lightbulb, hourglass, and more convoluted pearly shapes. It is found that more than one solution branch can be stable, and that negative curvature at the contact line of a pendant drop is not a prerequisite for instability. Numerical simulations based on the boundary-integral method for Stokes flow illustrate the process of unstable drop detachment. Unstable drops transform into elongated threads with a spherical head whose volume is determined by a Bond number expressing the significance of surface tension. A complementary investigation of the shape and stability of two-dimensional drops attached to a horizontal or inclined plane reveals that hydrostatic shapes are least stable in the inclined configuration and most stable in the pendant or sessile configuration.

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References

  1. Bashforth F, Adams JC (1883) An attempt to test the theories of capillary attraction. Cambridge University Press, Cambridge

    Google Scholar 

  2. Padday JF (1971) The profiles of axially symmetric menisci. Philos Trans R Soc Lond A 269: 265–293

    Article  ADS  Google Scholar 

  3. Padday JF, Pitt AR (1971) Axisymmetric meniscus profiles. J Colloid Interface Sci 38: 323–334

    Article  Google Scholar 

  4. Hartland S, Harley RW (1976) Axisymmetric fluid interfaces. Elsevier, Amsterdam

    MATH  Google Scholar 

  5. O’Brien SBG (1991) On the shape of small sessile and pendant drops by singular perturbation techniques. J Fluid Mech 233: 519–537

    Article  MathSciNet  ADS  MATH  Google Scholar 

  6. O’Brien SBG (1994) Asymptotic solutions for double pendant and extended sessile drops. Q Appl Math 52: 43–48

    MathSciNet  MATH  Google Scholar 

  7. Finn R (1986) Equilibrium capillary surfaces. Springer-Verlag, New York

    Book  MATH  Google Scholar 

  8. Homentcovschi D, Geer J, Singler T (1998) Uniform asymptotic solutions for small and large sessile drops. Acta Mech 128: 141–171

    Article  MathSciNet  MATH  Google Scholar 

  9. Finn R (2002) Some properties of capillary surfaces. Milan J Math 70: 1–23

    Article  MathSciNet  MATH  Google Scholar 

  10. Ferri JK, Kotsmar C, Miller R (2010) From surfactant adsorption kinetics to asymmetric nanomembrane mechanics: pendant drop experiments with subphase exchange. Adv Colloid Interface Sci. doi:10.1016/j.cis.2010.08.002

  11. Padday JF, Pitt AR (1973) The stability of axisymmetric menisci. Philos Trans R Soc Lond A 275: 489–528

    Article  ADS  Google Scholar 

  12. Schulkes RMSM (1994) The evolution and bifurcation of a pendant drop. J Fluid Mech 278: 83–100

    Article  MathSciNet  ADS  MATH  Google Scholar 

  13. Henderson D, Pritchard WG, Smolka LB (1999) On the pinch-off of a pendant drop of viscous fluid. Phys Fluids 9: 3188–3200

    Article  ADS  Google Scholar 

  14. Lowry BJ, Steen PH (1995) Capillary surfaces: stability from families of equilibria with application to the liquid bridge. Proc R Soc Lond A 449: 411–439

    Article  ADS  MATH  Google Scholar 

  15. Boucher EA, Evans MJB (1975) Pendent drop profiles and related capillary phenomena. Proc R Soc Lond A 346: 349–374

    Article  ADS  Google Scholar 

  16. Boucher EA, Evans MJB, Kent HJ (1976) Capillary phenomena. II. Equilibrium and stability of rotationally symmetric fluid bodies. Proc R Soc Lond A 349: 81–100

    Article  ADS  Google Scholar 

  17. Boucher EA (1980) Capillary phenomena: properties of systems with fluid/fluid interfaces. Rep Prog Phys 43: 497–546

    Article  MathSciNet  ADS  Google Scholar 

  18. Wente HC (1980) The stability of the axially symmetric pendent drop. Pac J Math 88: 421–470

    MathSciNet  MATH  Google Scholar 

  19. Pozrikidis C (2011) Introduction to theoretical and computational fluid dynamics, 2nd edn. Oxford University Press, Oxford

    MATH  Google Scholar 

  20. Pozrikidis C (2009) Fluid dynamics: theory, computation and numerical simulation, 2nd edn. Kluwer Academic Publishers, Norwell

    MATH  Google Scholar 

  21. Pozrikidis C (2008) Numerical computation in science and engineering, 2nd edn. Oxford University Press, Oxford

    MATH  Google Scholar 

  22. Pozrikidis C (1992) Boundary integral and singularity methods for linearized viscous flow. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  23. Pozrikidis C (2001) A practical guide to boundary-element methods with the software library BEMLIB. Chapman & Hall/CRC, Boca Raton

    Google Scholar 

  24. Papageorgiou DT (1995) Analytical description of the breakup of liquid jets. J Fluid Mech 301: 109–132

    Article  MathSciNet  ADS  MATH  Google Scholar 

  25. Chen TY, Tsamopoulos JA, Good RJ (1992) Capillary bridges between parallel and non-parallel surfaces and their stability. J Colloid Interface Sci 151: 49–69

    Article  Google Scholar 

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  1. Department of Chemical Engineering, University of Massachusetts, Amherst, MA, 01003, USA

    C. Pozrikidis

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  1. C. Pozrikidis
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Pozrikidis, C. Stability of sessile and pendant liquid drops. J Eng Math 72, 1–20 (2012). https://doi.org/10.1007/s10665-011-9459-3

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  • DOI: https://doi.org/10.1007/s10665-011-9459-3

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